"More accurately, "Lucifer Wannabe Frost," this demon doesn't actually have much to do with Lucifer. A Jack Frost who betrayed the Frost clan, he was exiled to Hell, where he saw Lucifer frozen in his lake of tears. Believing that this demon was the fabled "Snow Overlord" he was searching for, he tried many different things and was eventually able to impersonate Lucifer. He then returned to Hell to become Lucifer's minion, but by then Lucifer had vanished."

—Devil Summoner: Soul Hackers 3DS Compendium

Lucifrost is a demon exclusive to the 3DS remake, available at the very end of Nemechi's female growth path, and costs 500 D-Souls. Lucifrost is the highest level Herald, just exceeding Metatron by one level. He is in many ways a counterpart to Izanami, the equivalent at the end of the male Nemechi growth path.

LuciFroz is a level 60 boss type demon that the player can get after beating the game once. He is in the Ice Temple behind King Icy. If there is an empty space and one enters the correct password Dark he will join.

"More accurately, 'Lucifer Wannabe Frost', this demon doesn't actually have much to do with Lucifer.A Jack Frost who betrayed the Frost clan, he was exiled to Hell, where he saw Lucifer frozen in his lake of tears. Believeing that this demon was the fabled 'Snow Overlord' he was searching for, he tried many different things and was eventually able to impersonate Lucifer. He then returned to Hell to become Lucifer's minion, but by then Lucifer had vanished."